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Question: I Encountered Error Message trying to use dsolve to solve System of ODE with Parameters

Question:I Encountered Error Message trying to use dsolve to solve System of ODE with Parameters

Elisha 35 Maple 2018
ode parameters dsolve numeric differential-equations
February 11 2023
0

I find it difficult to use dsolve to solve system of ordinary differential equations with assigned parameters and initial conditions. The error message "Error, (in dsolve/numeric) 'parameters' must be specified as a list of unique unassigned names" kept coming up.

Pls see the uploaded equation for more understanding

> 

restart
> 

interface(imaginaryunit = F)

I

 (1)
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I

I

 (2)
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sqrt(-4)

2*I

 (3)
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NULL
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Suscep := diff(S(t), t) = theta*epsilon+v__2*S__v(t)-S(t)*lambda-S(t)*(µ+v__1)

diff(S(t), t) = theta*varepsilon+v__2*S__v(t)-S(t)*lambda-S(t)*(µ+v__1)

 (4)
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Vacc := diff(S__v(t), t) = (1-theta)*epsilon+v__1*S(t)-(µ+alpha+v__2)*S__v(t)-(1-w)*S__v(t)*lambda
> 

Immun := diff(V(t), t) = alpha*S__v(t)+`ρ__A`*A(t)+(1-k)*`ρ__Q`*Q(t)+`ρ__I`*(I)(t)-µ*V(t)
> 

Exp := diff(E(t), t) = S(t)*lambda+(1-w)*S__v(t)*lambda-(q__E+delta+µ)*E(t)
> 

Asymp := diff(A(t), t) = delta*a*E(t)-(`ρ__A`+µ)*A(t)+k*`ρ__Q`*Q(t)
> 

Inf := diff((I)(t), t) = delta*(1-a)*E(t)-(`ρ__I`+q__I+`δ__I`+µ)*(I)(t)
> 

Quar := diff((I)(t), t) = q__E*E(t)+q__I*(I)(t)-(`ρ__Q`+`δ__Q`+µ)*Q(t)
> 

init_conds := S(0) = S_0, S__v(0) = S__v*_0, V(0) = V_0, E(0) = E_0, A(0) = A_0, (I)(0) = I_0, Q(0) = Q_0

S(0) = S_0, S__v(0) = S__v*_0, V(0) = V_0, E(0) = E_0, A(0) = A_0, I(0) = I_0, Q(0) = Q_0

 (5)
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sys := {Asymp, Exp, Immun, Inf, Quar, Suscep, Vacc, init_conds}
> 

``
> 

sol := dsolve(sys, numeric, parameters = [`δ__Q`, `δ__I`, a, k, epsilon, v[1], q[E], q[I], q[A], eta[A], eta[Q], rho[A], rho[Q], rho[I], v[2], alpha, mu, delta, alpha, beta, w, lambda, S_0, S__v*_0, V_0, E_0, A_0, I_0, Q_0], method = rkf45)

Error, (in dsolve/numeric) 'parameters' must be specified as a list of unique unassigned names

  
> 

sol(parameters = [delta = .125, `δ__Q` = 0.6847e-3, epsilon = .464360344, `δ__I` = 0.2230e-8, a = .6255, q[E] = 0.18113e-3, k = .15, v__1 = 0.5e-1, v__2 = 0.6e-1, `ρ__Q` = 0.815e-1, `ρ__A` = .1, `ρ__I` = 0.666666e-1, q__I = 0.1923e-2, q__A = 0.4013e-7, `η__A` = .1213, `η__Q` = 0.3808e-2*alpha and 0.3808e-2*alpha = .4, w = .5925, mu = 0.464360344e-4, lambda = 0.1598643e-7, S_0 = 1.0, S__v*_0 = 0.6e-4, V_0 = 0.35e-4, E_0 = 0.5e-4, I_0 = 0.32e-4, A_0 = 0.15e-4, Q_0 = 0.1e-4])

sol(parameters = [delta = .125, delta__Q = 0.6847e-3, varepsilon = .464360344, delta__I = 0.2230e-8, a = .6255, q[E] = 0.18113e-3, k = .15, v__1 = 0.5e-1, v__2 = 0.6e-1, rho__Q = 0.815e-1, rho__A = .1, rho__I = 0.666666e-1, q__I = 0.1923e-2, q__A = 0.4013e-7, eta__A = .1213, false, w = .5925, mu = 0.464360344e-4, lambda = 0.1598643e-7, S_0 = 1.0, S__v*_0 = 0.6e-4, V_0 = 0.35e-4, E_0 = 0.5e-4, I_0 = 0.32e-4, A_0 = 0.15e-4, Q_0 = 0.1e-4])

 (6)
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Evaluate*the*system*at*t = 2
> 

sol(2)

sol(2)

 (7)
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sol(1)

sol(1)

 (8)
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sol(.1)

sol(.1)

 (9)
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sol(.3)

sol(.3)

 (10)
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sol(.5)

sol(.5)

 (11)
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sol(.7)

sol(.7)

 (12)
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sol(.9)

sol(.9)

 (13)
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sol(1.1)

sol(1.1)

 (14)
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sol(1.3)

sol(1.3)

 (15)
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sol(1.5)

sol(1.5)

 (16)
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> 

 

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